Reaction mechanism and kinetics of the degradation of bromoxynil initiated by OH radical

Abstract

Bromoxynil is a selective foliage herbicide used to control weeds. The degradation of bromoxynil in the atmosphere takes place dominantly via reaction with OH radicals. In this work, the OH initiated reactions of bromoxynil is studied using density functional theory methods M06-2X, B3LYP and MPW1K with 6-311++G(d,p) basis set. The relative energy of the reactive species is also calculated at CCSD(T)/6-311+G(d,p) level of theory. The OH initiated reaction of bromoxynil is found to proceed through H-atom abstraction and OH addition reactions, leading to the formation of six intermediates. The reactions subsequent to the principal oxidation steps are studied and the different reaction pathways are modeled. The radicals formed in the initial and subsequent reactions have a greater ability to undergo self-coupling, which yields dioxin and dioxepine products. These products are shown to be highly toxic and carcinogenic. The kinetics of the most favorable initial reactions are studied using canonical variational transition state theory with small curvature tunneling corrections over the temperature range of 278–350 K. This study provides thermochemical and kinetic data for the oxidation of bromoxynil in the atmosphere and demonstrates the formation of significant pollutants through oxidation reactions and lifetime of bromoxynil in the atmosphere.

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1. Introduction

Pesticides are semi-volatile compounds that are distributed in the form of gas, aqueous and solid phases. They are emitted into the atmosphere through three main routes: vapor shift during application, post-application vapor losses from the surfaces of treated soil and plants and wind erosion of treated soil.^1–5 As a result of these transport processes, the pesticides can exist as vapors or along with soil particles in the atmosphere. The contamination of pesticides in the atmosphere will affect the health of living beings and environment. The main route for the pesticidal removal from the atmosphere is the wet or dry deposition to terrestrial and aquatic environments.^6,7 However, these deposition techniques do not always result in the detoxification of the initial compound. Apart from these dry and wet deposition methods, other removal mechanisms for pesticides include chemical reactions that are occurring in the atmosphere. The photochemical conversion of pesticides is enhanced by reaction with atmospheric oxidants such as hydroxyl, ozone and nitrate radicals.⁸ These biotic and abiotic transformations may efficiently remove pesticides from the environment, but may give rise to potentially hazardous products.⁹

Herbicides are a group of pesticides used to prevent the growth of unwanted plants. Bromoxynil is a selective contact foliage herbicide used to control a variety of broadleaf weeds. It acts as a photosynthetic electron transport inhibitor, thereby stopping energy production without affecting plant respiration. Bromoxynil is dispersed in the atmosphere by microbes and also by sunlight. The effect of bromoxynil on ground water and soil is low, whereas in the atmosphere, the spreading of bromoxynil is of potential importance due to its high volatality.¹⁰ The presence of nitrile group in the bromoxynil is highly toxic and is an extremely potent metabolic poison.¹¹ Unlike other herbicides and pesticides, bromoxynil has no chiral property, hence the soil microbes prefer to consume the optically inactive bromoxynil. This can have unpredictable effect on the rate at which these organochemicals can be removed from the environment.¹² The abiotic degradation of bromoxynil in the atmosphere is mainly due to photolysis reaction with OH radical.¹³ The OH radical is a potent atmospheric oxidizing agent.¹⁴ As shown in Fig. 1, bromoxynil has many reactive sites for the reaction with OH radical. The H-atom abstraction from the OH group of bromoxynil results in the formation of unstable phenoxy radical which undergoes reaction with other atmospheric species such as NO, NO₂, O₂, etc. The phenoxy radical can undergo self-reaction resulting in the formation of brominated dibenzo-p-dioxins. These brominated compounds are considered as the most dangerous persistent organic pollutants (POP).¹⁵ The boiling point of brominated dibenzo-p-dioxins range from 310 to 425 °C¹⁶ and hence they are semi volatile organic compounds, which causes adverse effects on human health.¹⁷ That is, these halogenated POPs are more rapidly metabolized¹⁸ and are found to form reactive metabolite intermediates such as epoxides, dihydroxy aromatics and quinones, the products which are highly carcinogenic. Further, OH initiated reaction of bromoxynil leads to the formation of HOBr which is the potential source for the carcinogenic bromate ions. The reaction between bromoxynil and OH radical can lead to many hazardous gaseous pollutants including the highly toxic hydrogen cyanide. The reaction between OH radical and bromoxynil can also proceed by the electrophilic addition of OH radical to the bromoxynil, which on subsequent reaction with O₂ leads to the formation of ring opening and ring rearrangement products. These products usually relate to hazardous pollutants. Many recent studies have focused on the oxidation and transformation of chlorinated compounds in the atmosphere.^19–22 But, the study of brominated compounds is very scarce in the literature.

Fig. 1 The optimized structure of the bromoxynil + OH reaction system.

In spite of the relative importance of the products formed from the atmospheric degradation of bromoxynil, there are only few experimental data available on the kinetics of the reaction of bromoxynil with OH radical.^13,23 But, no study focused on the mechanism and pathways involved in the reaction of bromoxynil with OH radical and on subsequent secondary reactions. The elucidation of reaction mechanism using experimental methods is very difficult because of the ambiguity in detecting the unstable intermediates and transition states, whereas quantum chemical methods provide an efficient way to determine the reaction intermediates and pathways. The aim of this work is to elucidate the reaction between bromoxynil and OH radical using quantum chemical methods. The energy barriers and reaction enthalpies are calculated to assess the energetically favorable reaction pathways and stability of the products. Subsequently, the rate constant and branching ratios of the product channels are calculated using variational transition state theory (VTST). This study will provide an improved understanding on the formation of toxic pollutants from bromoxynil. From the results obtained, the environmental implications of the bromoxynil degradation are discussed.

2. Computational details

The geometry optimization of the reactant, transition states, intermediates and products were performed using density functional theory methods, M06-2X,²⁴ B3LYP^25,26 and MPW1K²⁷ with 6-311++G(d,p) basis set. The hybrid density functional B3LYP is the most widely used method for studying the chemical reactions.^28,29 The MPW1K method is a competitive method in predicting the energies and geometries of the stationary points along the minimum energy path and provides promising accuracy for the calculation of reaction energies and kinetics.³⁰ Recent studies show that DFT calculations with M06-2X functional perform well for thermochemical and reaction mechanism studies.^31,32 Hence, in the present work we employed the above three DFT functionals to study the reaction mechanism and kinetics. Harmonic vibrational frequencies were calculated at the same level of theories to determine the nature of the stationary points. All minima were confirmed with all positive frequencies and each transition state had one imaginary frequency confirming its maxima in one reaction coordinate. For all the studied reactions, the connectivity between the transition state and its corresponding reactant and product was verified by performing intrinsic reaction coordinate (IRC) calculations.³³ The paths have been verified by following the Gonzalez–Schlegel steepest descent path in mass-weighted internal coordinates.³⁴ Since, a recent study³⁵ has shown that the M06-2X functional is able to reproduce the results obtained at CCSD(T) calculations with sufficient accuracy for all the stationary points on the ground state PES, electron correlation was accounted by performing single-point energy calculations at coupled cluster method with single and double substitutions with noniterative triple excitations, CCSD(T)³⁶ using 6-311+G(d,p) basis set with the geometries optimized at M06-2X/6-311++G(d,p) level of theory. The enthalpy of reaction and Gibb's free energy values were calculated by including thermodynamic corrections to the energy at 298.15 K and at 1 atmospheric pressure. All the electronic structure calculations were performed using Gaussian 09 program package.³⁷

The computed potential energy surface and associated transition state parameters were directly utilized to predict the rate constant as a function of temperature. The theoretical rate constants for the reactions are calculated using canonical variational transition state theory (CVT) from which the rate constant is given by the formula,

k^CVT(T) = min_Rk^GT(T,s) (1)

where,where k^GT(T,s) is the generalized transition state theory rate constant, σ is the symmetry factor accounting for the possibility of more than one symmetry related reaction path, Q_c(T,s) is the classical partition function for the generalized transition state dividing surface, ϕ_c(T) is the reactant partition function per unit volume, V_MEP(s) is the classical potential energy at point s on the minimum energy path, k_B is Boltzmann's constant, and h is Planck's constant. The quantity (βh)⁻¹ is called the universal transition state frequency factor. Since the CVT rate constant neglects the tunneling, it underestimates the rate constant for the reactions in which quantum tunneling is predominant, especially at low temperatures. Hence, in order to account for the dynamical quantum effects of reaction-coordinate tunneling, a multiplicative transmission coefficient κ(T) is used in eqn (1) as

k^CVT_c(T) = κ(T)k^CVT(T) (3)

The transmission coefficient κ(T) corresponding to tunneling is evaluated by small-curvature approximation to the vibrational adiabatic potential energy surface. In this approximation, the tunneling is assumed to occur along a multi-dimensional minimum energy path. The potential energy curve is approximated by a contracted adiabatic energy barrier which goes through the ZPVE corrected energy of the reactants, transition states and products. The kinetic calculations are carried out using Gaussrate2009A³⁸ program which is an interface program between Gaussian 09 and Polyrate 2010A programs.³⁹

3. Results and discussion

3.1 OH-initiated reactions

The reaction of bromoxynil with OH radical under atmospheric conditions is initiated in two different ways: H-atom abstraction by OH radical and electrophilic addition of OH radical to the aromatic ring of bromoxynil. The optimized structure of the bromoxynil + OH reaction system is illustrated in Fig. 1. The reaction scheme for the OH initiated reactions of bromoxynil is depicted in Fig. 2. As shown in Fig. 2, six different intermediates are formed due to the addition and abstraction reactions. In bromoxynil, the phenol group donates the electrons into the ring by resonance and favors the OH radical attack at para position of bromoxynil. The OH radical addition reaction leads to the formation of 3,5-dibromo-2,4-dihydroxy benzonitrile (I1). The OH radical abstracts the H-atom from the phenol group or from the aromatic ring of bromoxynil, leading to the formation of 2,6-dibromo-4-cyanophenoxy radical (I2) or 2,6-dibromo-4-cyano-1-hydroxy benzene radical (I3). The OH radical undergoes radical termination reaction in which the Br-atom attached to the bromoxynil is abstracted by the H-atom of OH radical resulting in the formation of hydrogen bromide and the O-atom of OH radical binds with C-radical site in bromoxynil resulting in the formation of 5-bromo-4-hydroxy-3-oxocyclohexa-1,5-diene carbonitrile (I4). In one of the reactions, the O-atom of OH radical binds with the Br-atom of bromoxynil and thus 3-bromosyl-5-cyano-2-hydroxybenzene radical (I5) is formed. Also, in the radical termination reaction, the H-atom abstracts the cyano group of bromoxynil leading to the formation of hydrogen cyanide and the O-atom of OH radical binds with the C-radical site of bromoxynil, resulting in the formation of 3,5-dibromo-4-hydroxycyclohexa-2,4-dienone (I6). Thus six different intermediates are formed and each intermediate has its own impact in the environment by undergoing subsequent reactions with other atmospheric oxidants. The formation of intermediates, I4 and I5 indicates that halogen displacement occurs in gas-phase reactions of halogenated aryls with electrophilic radicals.⁴⁰ The relative energy of the reactive species for the initial oxidation steps calculated using M06-2X/6-311++G(d,p) and CCSD(T)/6-311+G(d,p)//M06-2X/6-311++G(d,p) level of theories is summarized in Table 1. From Table 1, it is observed that the energetics calculated using the two methods are comparable. This result shows the reliability of the present calculations. Further, the reactive species are also optimized at B3LYP and MPW1K methods with 6-311++G(d,p) basis set. The energetics obtained using B3LYP and MPW1K methods are summarized in Tables S1–S4 of ESI.† The structural parameters of the reactive species obtained from the above three DFT methods differ slightly. For instance, the rmsd between the internal coordinates obtained using M06-2X and B3LYP methods is 0.09 Å, 0.02 Å and 0.1 Å, respectively for the reactant, transition state and product. The rmsd between the internal coordinates obtained from M06-2X and MPW1K methods is 0.01 Å, 0.03 Å and 0.03 Å, for the reactant, transition state and product, respectively. Note that the above mentioned rmsd values include interactions of both bonded and non-bonded atoms. In most of the cases, the energetics obtained with the three DFT functionals are comparable [see Tables 1–4 and S1–S4†]. On comparing the results obtained for various reaction paths, it is observed that the relative importance of the various reaction channels does not change with respect to the methods of calculation. The favorable reaction path in the studied reaction pathways is the same in the three DFT methods. In recent studies, the M06-2X functional has been shown to give reliable barrier heights and the rate constant calculated using the energetics obtained with M06-2X functional is in good agreement with experimental results.^41,42 Hence, the structure and energetics obtained using M06-2X functional with 6-311++G(d,p) basis set are discussed in detail and are used in further kinetic calculations. The pathways for the formation of the intermediates and their subsequent reactions are discussed below. The optimized structures of the transition states involved in the reactions are illustrated in Fig. S1 of ESI.† The relative energy, enthalpy of reaction and Gibb's free energy of the reactive species optimized at M06-2X/6-311++G(d,p) level of theory are summarized in Table 1. The Table 1 shows that all the initial reactions are exothermic and exoergic.

Fig. 2 Reaction scheme corresponding to the initial oxidation of bromoxynil by OH radical.

Table 1 Relative energy (ΔE in kcal mol⁻¹), enthalpy of reaction (ΔH in kcal mol⁻¹) and Gibb's free energy (ΔG in kcal mol⁻¹) of the reactive species involved in the initial oxidation reaction of bromoxynil by OH radical

Reactive species	M06-2X/6-311++G(d,p)			CCSD(T)/6-311+G(d,p)
	ΔE	ΔH	ΔG	ΔE
R	0.0	0.0	0.0	0.0
TS1	0.85	0.38	0.52	2.2
I1	−18.08	−15.8	−13.43	−18.64
TS2	7.31	4.6	6.17	7.86
I2	−26.62	−26.69	−27.79	−29.85
TS3	13.78	9.72	9.81	11.55
I3	−3.73	−3.5	−4.68	−2.1
TS4	53.0	46.9	55.32	54.2
I4	−96.45	−93.94	−92.28	−96.93
TS5	50.83	47.48	49.6	50.56
I5	−25.81	−26.6	−26.75	−26.36
TS6	81.17	76.85	78.87	77.03
I6	−20.16	−20.09	−21.64	−20.8

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The relative energy profile for the initial reactions is illustrated in Fig. 3. The intermediate, I1 is formed through a transition state, TS1 with a small energy barrier of 0.85 kcal mol⁻¹. In the transition state structure, TS1, the distance between the O-atom of OH radical and carbon-atom of bromoxynil to which the OH radical is added has decreased by 0.8 Å from that of the reactants. The H-atom abstraction reactions lead to the formation of phenoxy, I2 and benzene radical, I3 intermediates along with the elimination of H₂O molecule through transition states, TS2 and TS3 with energy barriers of 7.31 and 13.8 kcal mol⁻¹, respectively. As shown in Fig. S1,† in the TS2 structure, a H-bond of length 1.06 Å exists between the O-atom of OH radical and the abstracted H-atom of phenol group. This transition state is a consequence of the π-type hydrogen bond interaction. In the TS3 structure, the H-atom attached to the C-atom of aromatic ring is abstracted by the OH radical and the bond length of the newly formed O₂–H₂ bond is 1.21 Å [For labeling of atoms see Fig. 1 and S1†]. The formation of intermediate, I4 occurs via a transition state, TS4 with an energy barrier of 53 kcal mol⁻¹. The TS4 is a late transition state in which the O-atom of OH radical binds with the carbon radical site from which Br-atom was abstracted. As shown in Fig. 3, the intermediate, I5 is formed through a transition state, TS5 with an energy barrier of 50.83 kcal mol⁻¹. That is, TS5 is also a late transition state in which the structural parameters deviate much from the reactants and the transition state is product like. The formation of hydrogen cyanide along with 3,5-dibromo-4-hydroxycyclohexa-2,4-dienone, I6 requires a large energy barrier of 81.17 kcal mol⁻¹ through a transition state, TS6. The transition state, TS6 is product like with large structural change from that of the reactants. The above results show that the formation of intermediates, I4, I5 and I6 are the rate-determining steps and does not contribute significantly to the overall environmental evolution of bromoxynil. Hence, the subsequent reactions of the intermediates, I1, I2 and I3 are studied in detail.

Fig. 3 Relative energy profile corresponding to the initial oxidation of bromoxynil by OH radical.

3.2 Subsequent reactions from intermediate, I1

The reaction scheme for the subsequent reactions from the intermediate, I1 is given in Fig. 4. The relative energy profile of the subsequent reactions from I1 is shown in Fig. 5. The relative energy, enthalpy of reaction and Gibb's free energy of the reactive species are summarized in Table 2. The radicals formed in the initial oxidation of bromoxynil by OH radical are prone to undergo subsequent reaction with molecular oxygen present in the atmosphere. The reaction between the intermediate, I1 and O₂ results in the formation of peroxy and epoxy radicals. As shown in Fig. 5, the peroxy radical intermediate, I7 is formed through a transition state, TS7 with an energy barrier of 10.82 kcal mol⁻¹ and with a reaction enthalpy of −1.2 kcal mol⁻¹. In this intermediate, the O₂ molecule binds with the C-atom at the ortho position of the aromatic ring and thus a peroxy radical is formed. This result is in consistent with a previous theoretical study on the reaction between benzene–OH adduct and O₂ in which the O₂ addition occurs preferentially at the ortho position of the aromatic ring.⁴³ The intermediate, I7 further reacts with HO₂ in the atmosphere. The secondary reactions of peroxy radical with HO₂ slow down the free radical driven photochemical oxidation reactions and reduce the formation of ozone.⁴⁴ Also, these reactions represent an important chemical sink for HO_x radicals in the troposphere. Hence, the reaction between peroxy radical and HO₂ is of comparable importance in determining the fate of bromoxynil. This reaction results in the formation of hydroperoxide adduct and O₂ (P1) through a transition state, TS8 with an energy barrier of 52.83 kcal mol⁻¹. The transition state structure, TS8 is a late transition state in which an H-bonding interaction is observed between the O₃ and H₄-atoms with a hydrogen bond length of 2.04 Å. Further, the distance between H₅ and O₃-atoms has decreased by about 2 Å from that of the reactants. Thus, in this case, the H-atom addition to peroxy radical site is not feasible as observed in the transformation of BDE-15 (Brominated diphenyl ether) by OH radical and further reaction with O₂.⁴⁵ In polluted areas, there is a significant concentration of nitrogen oxides. At ambient conditions, the reaction of peroxy radical with NO is generally fast. In the reaction between intermediate, I7 and NO, NO is oxidized to NO₂ and an alkoxy radical intermediate, I8 is formed. This oxidation reaction is of potential importance because the NO₂ so formed involves in the depletion of atmospheric ozone.⁴⁶ This reaction occurs through a transition state, TS9 with an energy barrier of 7.8 kcal mol⁻¹. On comparing the energy barrier for the reaction of peroxy radical (I7) with HO₂ and NO, it is observed that the reaction between I7 and HO₂ is not competitive in determining the fate of bromoxynil. As summarized in Table 2, the reactions of I7 with HO₂ and NO occur in mild endothermic and endoergic processes.

Fig. 4 Reaction scheme corresponding to the subsequent reactions from 3,5-dibromo-2,4-dihydroxy benzonitrile intermediate (I1).

Fig. 5 Relative energy profile corresponding to the subsequent reactions from 3,5-dibromo-2,4-dihydroxy benzonitrile intermediate (I1).

Table 2 Relative energy (ΔE in kcal mol⁻¹), enthalpy of reaction (ΔH in kcal mol⁻¹) and Gibb's free energy (ΔG in kcal mol⁻¹) of the reactive species involved in the subsequent reaction of the intermediate, I1 calculated at M06-2X/6-311++G(d,p) level of theory

Reactive species	ΔE	ΔH	ΔG
I1 + O2	0.0	0.0	0.0
TS7	10.82	11.58	15.26
I7	−3.82	−1.2	−2.67
I7 + HO2	0.0	0.0	0.0
TS8	52.83	50.47	49.41
P1	4.22	3.04	0.15
I7 + NO	0.0	0.0	0.0
TS9	7.8	7.7	6.5
I8	1.31	1.33	1.91
I1 + O2	0.0	0.0	0.0
TS10	7.36	6.32	10.84
I9	−25.88	−26.95	−24.2
I9	0.0	0.0	0.0
TS11	12.23	14.31	16.6
P2	−16.38	−17.08	−20.7
I1 + O2	0.0	0.0	0.0
TS12	24.66	26.7	32.5
I10	−4.82	−2.35	−2.28
TS13	13.61	15.22	20.68
I11	−6.44	−4.16	−3.05

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As shown in Fig. 4, the reaction between O₂ and I1 also leads to the formation of epoxy radical, I9 and two bicyclic radicals, I10 and I11. In the intermediate, I9, one of the oxygen atoms of O₂ binds between the C-atom to which the OH radical is attached and the adjacent C-atom to which Br-atom is attached and the other O-atom binds with the Br-atom. Thus a seven-membered ring intermediate is formed. This intermediate is formed through a transition state, TS10 with an energy barrier of 7.36 kcal mol⁻¹. As shown in Fig. S1,† in the TS10 structure, the bond between the O-atoms of O₂ is broken and the O-atoms are attached to the C-atoms to which Br-atoms are bonded. The intermediate, I9 further decomposes into a dihydroxy epoxy product, along with HOBr (P2). The HOBr is identified as a major source for the formation of bromated ion, which is a potential carcinogenic product.⁴⁷ This decomposition is associated with a transition state, TS11 with an energy barrier of 12.23 kcal mol⁻¹. These dihydroxy epoxy products are identified as recognized metabolites of polybrominated or polychlorinated compounds in the atmosphere.⁴⁸ Hence, this reaction is of environmental significance. As shown in Fig. 4, the bicyclic radical, I10 is formed by the binding of O₂ molecule with the ortho and meta position C-atoms of the aromatic ring. This radical is formed through a transition state, TS12 with an energy barrier of 24.66 kcal mol⁻¹. In TS12, the O₄-atom binds with the meta C-atom and the O₃-atom makes a hydrogen bonding with the H₄-atom of I7 [see Fig. S1†]. The distance between the O₃-atom and the ortho C-atom is 2.05 Å which was 3.26 Å in the reactant. The bicyclic radical, I11 is formed by the binding of O₂ molecule with the meta and para position C-atoms through a transition state, TS13 with an energy barrier of 13.61 kcal mol⁻¹. In the TS13 structure, the O3-atom of O₂ binds with the C-atom at meta position and the distance between the O₄-atom and para position C-atom is decreased by 1.56 Å from that of the reactants. These bicyclic radicals further decompose into ring opening products like butanedial, glyoxal, etc.,⁸ which are more hazardous than the parent bromoxynil. These products are responsible for the formation of low-volatile, secondary organic aerosol species.^49,50 As summarized in Table 2, the formation of peroxy radical is more exothermic and exoergic than the formation of bicyclic and epoxy radicals. The most favorable secondary reaction pathway from the intermediate, I1 is the formation of intermediate, I9 due to the small energy barrier of 7.36 kcal mol⁻¹.

3.3 Subsequent reactions from intermediate, I2

The reaction scheme for the subsequent reactions from intermediate, I2 is shown in Fig. 6. The relative energy profile of the subsequent reactions from intermediate, I2 is illustrated in Fig. 7. The relative energy, enthalpy of reaction and Gibb's free energy of the reactive species are summarized in Table 3. The phenoxy radical intermediate, I2 undergoes self-reaction leading to the formation of tribromo-dibenzo-dioxin-dicarbonitrile (TBDDD) and tetrabromo-tetrahydrobenzo-cyclopenta-dioxepine-dicarbonitrile (TeBDD). The dimerization of the phenoxy radical is found to be the major reaction pathway in the homogeneous gas formation of dibenzo-dioxins,⁵¹ which are highly toxic and carcinogenic.⁵² It has been shown in an earlier study, that the ring closure of predioxins (precursors of dioxins) takes place through intramolecular condensation.⁵³ Since, the intermediate, I2, which is a predioxin is formed with a small energy barrier, its self-coupling reaction exhibits condensation under ambient atmospheric conditions. The formation of dioxin products involves o-phenoxy-phenol (POP) intermediates.^51,54 I2 is an oxygen-centered delocalized radical mesomer which can couple with the ortho carbon atom of its self-reactant, resulting in POP intermediate, I12. Here, the nucleophilic attack of the phenolic oxygen atom at the neighboring phenoxy radical is facilitated during the formation of I12 by the withdrawal of electron density from the aromatic ring by bromine atoms. The intermediate, I12 is formed by the coupling of O-radical of I2 with the C-atom at the ortho position of the adjacent I2 through a transition state, TS14 with a small energy barrier of 1.54 kcal mol⁻¹. In the transition state structure, TS14, the distance between the O radical of I2 and the ortho C-atom of the self-reactant has decreased by 1.55 Å from that of the reactants. As given in Table 3, this intermediate formation is exothermic and exoergic by −24.05 and −24.36 kcal mol⁻¹, respectively. The intermediate, I12 then undergoes intra-annular elimination of hydrogen bromide resulting in the formation of TBDDD, the product channel P3 [see Fig. 6]. Similar compounds were observed in the fly ash samples of municipal waste incinerators.⁵⁵ This reaction occurs via a transition state, TS15 with an energy barrier of 13.95 kcal mol⁻¹. This reaction is strongly exothermic and exoergic with reaction enthalpy of −81.26 kcal mol⁻¹ and free energy of −79.02 kcal mol⁻¹, respectively.

Fig. 6 Reaction scheme corresponding to the subsequent reactions from 2,6-dibromo-4-cyanophenoxy radical (I2).

Fig. 7 Relative energy profile corresponding to the subsequent reactions from 2,6-dibromo-4-cyanophenoxy radical (I2).

Table 3 Relative energy (ΔE in kcal mol⁻¹), enthalpy of reaction (ΔH in kcal mol⁻¹) and Gibb's free energy (ΔG in kcal mol⁻¹) of the reactive species involved in the subsequent reaction of the intermediate, I2 calculated at M06-2X/6-311++G(d,p) level of theory

Reactive species	ΔE	ΔH	ΔG
I2 + I2	0.0	0.0	0.0
TS14	1.54	1.27	2.45
I12	−25.18	−24.05	−24.36
TS15	13.95	14.32	13.12
P3	−83.31	−81.26	−79.02
I2 + I2	0.0	0.0	0.0
I13	−12.58	−13.16	−12.34
TS16	7.35	8.12	7.65
I14	−89.8	−81.65	−77.75
TS17	11.52	12.33	11.17
P4	−93.35	−90.41	−88.61
I2 + NO2	0.0	0.0	0.0
TS18	21.12	19.77	20.27
P5	1.24	2.15	1.97

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The formation of TeBDD is based on ortho–ortho coupling of phenoxy radicals. The ortho–ortho coupling of I2 results in the formation of intermediate, I13 in a barrierless reaction. This intermediate is formed in an exothermic and exoergic reaction with ΔH = −13.16 kcal mol⁻¹ and ΔG = −12.34 kcal mol⁻¹, respectively. This intermediate is followed by intra-annular elimination of H₂ molecule leading to another intermediate, I14 through a transition state, TS16 with an energy barrier of 7.35 kcal mol⁻¹. In this reaction, the H-atoms attached to the C-atoms at meta and para positions are eliminated and H₂ molecule is formed. In TS16, the H₂ molecule is eliminated and the bond distance between the H-atoms of H₂ is 0.73 Å. The intermediates, I13 and I14 are semiquinone radicals⁵⁶ that are determining the toxicity of brominated compounds. Since, no bromine atoms are eliminated in the formation of I13 and I14, these intermediates are more stable than the parent bromoxynil. Then, in the next step, the ring closure produces TeBDD, P4. As shown in Fig. 7, this product formation is characterized by a transition state, TS17 with an energy barrier of 11.52 kcal mol⁻¹. The intermediate, I14 and the product, P4 are formed with high exothermicity and exoergicity [see Table 3].

In highly pollutant areas, where NO₂ is abundantly present, the intermediate, I2 reacts with NO₂ in a mild endothermic reaction yielding nitroso bromoxynil, P5. This product formation is characterized by a transition state, TS18 with an energy barrier of 21.12 kcal mol⁻¹. In the transition state structure, the distance between the O-radical of I2 and N-atom of NO₂ is 1.47 Å, which was 2.87 Å in the reactants [see Fig. S1†]. This product is formed in a mild endothermic and endoergic reaction. Of all the secondary reactions studied from the intermediate, I2, the most favorable pathway is the formation of TeBDD, P4 product channel.

3.4 Subsequent reactions from intermediate, I3

The reaction scheme for the subsequent reactions from intermediate, I3 is illustrated in Fig. 8. The relative energy profile corresponding to the secondary reactions from I3 is shown in Fig. 9. The relative energy, enthalpy of reaction and Gibb's free energy of the reactive species are summarized in Table 4. The benzene radical, I3 is found to be highly active and plays an important role in the formation of various pollutants.^57,58 The benzene radical, I3 subsequently reacts with O₂ resulting in the formation of peroxy radical intermediate, I15 in a barrierless reaction. The potential energy surface (PES) for this reaction was studied by varying the C–O bond length. The PES scan result showed that along the reaction coordinate, there are no stationary points with energy greater than C–O bond dissociation energy. This reveals that there is no transition state in the formation of peroxy radical, I15. As summarized in Table 4, this intermediate is formed spontaneously and ΔH is only 0.87 kcal mol⁻¹. The peroxy radical, I15 further transforms into new products that were not observed for the peroxy radical formed from the intermediate, I1. There are three promising pathways identified for the exit pathway for the peroxy radical, I15. The peroxy radical reacts with HO₂ resulting in the formation of hydroperoxide adduct, and O₂ (P6) through a transition state, TS19 with an energy barrier of 9.41 kcal mol⁻¹. In the transition state structure, TS19, the distance between the H-atom of HO₂ and the O-atom of peroxy radical has decreased by 1.32 Å from that of the reactants. As shown in Fig. 8, the peroxy radical intermediate, I15 oxidizes NO to NO₂ along with the formation of alkoxy radical intermediate, I16. This reaction pathway is identified through a transition state, TS20 with an energy barrier of 24.91 kcal mol⁻¹. In TS20, the distance between the terminal O-atom of the peroxy radical site and the O-atom of NO is 2.19 Å, which was 3.76 Å in the reactants. The alkoxy radical intermediate has excess energy to undergo further oxidation reaction, resulting in the formation of carbonyl compounds. The next competing exit pathway for I15 is its reaction with NO₂ to form nitroso bromoxynil, P7. This reaction takes place via a transition state, TS21 with an energy barrier of 10.6 kcal mol⁻¹. In the transition state structure, TS21, the distance between the N-atom of NO₂ and the terminal O-atom of peroxy radical site has decreased by about 1.35 Å from that of the reactants. All these competitive exit pathways are exothermic and exoergic.

Fig. 8 Reaction scheme corresponding to the subsequent reactions from 2,6-dibromo-4-cyano-1-hydroxy benzene radical (I3).

Fig. 9 Relative energy profile corresponding to the subsequent reactions from 2,6-dibromo-4-cyano-1-hydroxy benzene radical (I3).

Table 4 Relative energy (ΔE in kcal mol⁻¹), enthalpy of reaction (ΔH in kcal mol⁻¹) and Gibb's free energy (ΔG in kcal mol⁻¹) of the reactive species involved in the subsequent reaction of the intermediate, I3 calculated at M06-2X/6-311++G(d,p) level of theory

Reactive species	ΔE	ΔH	ΔG
I3 + O2	0.0	0.0	0.0
I15	0.87	0.77	0.68
I15 + HO2	0.0	0.0	0.0
TS19	9.41	8.43	7.73
P6	−11.83	−10.17	−14.28
I15 + NO	0.0	0.0	0.0
TS20	24.91	23.5	22.52
I16	−33.0	−31.28	−30.43
I15 + NO2	0.0	0.0	0.0
TS21	10.6	9.98	10.53
P7	−26.07	−24.3	−23.18
I15 + I15	0.0	0.0	0.0
TS22	56.97	55.17	52.45
P8	−11.3	−12.0	−16.14

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An important property of the peroxy radical is its ability to undergo self-reaction. Hence, another possible reaction for the fate of peroxy radical intermediate, I15 is its self-coupling reaction, which results in the formation of brominated diphenyl ether, along with the O₃ molecule, P8 [see Fig. 8]. This product is analogous to the product 3,4,6-trichloro-3-(2,4,5-trichlorophenoxy) phenol formed from the self-reaction of 2,4,5-trichlorophenol.⁵⁹ In the product P8, electron density is delocalized over the diphenyl ether backbone. Here, the conjugation of the two aryl ring in the diphenyl ether occurs over the ether oxygen and depends on the steric and electron withdrawing property of the cyano group attached at the para position. That is, the cyano group at para positions facilitates the formation of a conformation in which the bridging oxygen π–lone pair conjugates with the π–electron system of the two rings. As shown in Fig. 9, this self-coupling reaction takes place through a transition state, TS22 with an energy barrier of 56.97 kcal mol⁻¹ in an exothermic and exoergic reaction with ΔH = −12 kcal mol⁻¹ and ΔG = −16.14 kcal mol⁻¹, respectively. In the transition state structure, TS22, one O-atom from each peroxy radical binds with the para and ortho position C-atoms of the self-reactants. The remaining O-atoms form a bridge between the two self-reactants [see Fig. S1†]. As shown in Fig. 9, the most favorable secondary reaction pathway from the intermediate, I3 is the formation of hydroperoxide adduct along with O₂ in the P6 product channel.

3.5 Kinetics

The rate constant of the most favorable initial reactions (I1, I2 and I3) is calculated using CVT with SCT corrections over the temperature range of 278–350 K and at 1 atmospheric pressure. It is obvious from the energetics of the studied pathways, that under atmospheric conditions, the OH initiated reactions are the most important atmospheric degradation pathways for bromoxynil. The rate constant k_I1, k_I2 and k_I3 calculated using CVT/SCT method over the temperature range of 278–350 K for the formation of intermediates, I1, I2 and I3, respectively are summarized in Table 5. For comparison purposes, the rate constant calculated using transition state theory (TST) and CVT without tunneling corrections are summarized in Table S5 of ESI.† The Arrhenius plot showing the temperature dependence of the rate constant of the three intermediates is shown in Fig. S2.† The plot reveals that the rate constant show linear Arrhenius behavior. The rate constant calculated at 298 K for I1 is 7.43 × 10⁻²² cm³ molecule⁻¹ s⁻¹, which is quite comparable with the value of 9.5 × 10⁻²² cm³ molecule⁻¹ s⁻¹ calculated for the electrophilic addition reaction of OH radical to dimethylphenol in our previous study.⁶⁰ As given in Table S5,† the variational effect in the rate constant, k_I1 is negligible and the variational transition state is located at the reaction coordinate, s = −0.007 Å. The tunneling effect is also negligible for this intermediate formation due to the broad energy barrier as suggested by the small imaginary frequency of TS1 (−128.66 cm⁻¹). This initial reaction is reversible with a reverse rate constant of 9.92 × 10⁻²² cm³ molecule⁻¹ s⁻¹ at 298 K. The variation of k_I1 with temperature is very small which suggests that the activation energies around 298 K should be close to zero. The Arrhenius activation energy calculated for this initial step at 298 K is 3.88 kcal mol⁻¹.

Table 5 The rate constant, k_I1, k_I2 and k_I3 (cm³ molecule⁻¹ s⁻¹) calculated for the formation of intermediates, I1, I2 and I3 over the temperature range of 278–350 K using CVT/SCT method

Temperature (K)	kI1 (× 10^−22)	kI2 (× 10^−11)	kI3 (× 10^−20)
278	6.67	0.06	0.09
288	7.05	0.36	0.2
298	7.43	1.92	0.42
308	7.81	9.12	0.83
318	8.21	39.46	1.58
328	8.58	157.11	2.88
338	8.97	579.4	5.07
348	9.37	1991.7	8.66
350	9.45	2529.6	9.6

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At 298 K, the rate constant, k_I2 is 1.92 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹, which is quite comparable with the literature value of 9.4 × 10⁻¹² cm³ molecule⁻¹ s⁻¹, calculated for the H-atom abstraction from phenol by OH radical.⁶¹ A previous experimental study on the atmospheric oxidation of bromoxynil by ozonation reported a rate constant of 8.4 × 10⁹ M⁻¹ s⁻¹.²³ The reverse rate constant calculated for H-atom abstraction from phenol group of bromoxynil at 298 K is 8.87 × 10⁻²⁵ cm³ molecule⁻¹ s⁻¹. That is, the reversibility of this reaction is negligible which is reflected in the equilibrium constant value of 2.78 × 10¹⁰. The tunneling effect for this reaction is appreciable with a transmission coefficient of 20.87. As summarized in Table S5,† the ratio between the CVT and TST rate constant is 1, which shows that variational effect is negligible in this reaction. The variational transition state corresponding to this reaction is located at the reaction coordinate, s = −0.136 Å. The Arrhenius activation energy of 12.4 kcal mol⁻¹ is calculated for this reaction at 298 K. The forward rate constant, k_I3 calculated for the formation of intermediate, I3 at 298 K is 0.42 × 10⁻²⁰ cm³ molecule⁻¹ s⁻¹. The tunneling effect is negligible in this reaction due to the transmission coefficient of 1.8. The variational transition state corresponding to this reaction is located at s = 0.095 Å and variational effect is negligible for this reaction. The reverse rate constant for the formation of I3 at 298 K is 2.9 × 10⁻²⁸ cm³ molecule⁻¹ s⁻¹. The Arrhenius activation energy for I3 calculated at 298 K is 5.5 kcal mol⁻¹.

The branching ratio is calculated as the ratio between rate constant for particular intermediate formation reaction channels and the sum of the rate constants of all possible intermediate formation reaction channels studied. For example, for intermediate channel, I1 the branching ratio is,

where, i runs from 1 to 3, favorable intermediate channels studied. The overall rate constant at 298 K is 1.92 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹. Using, the overall rate constant in the above equation, it has been observed that the contribution of intermediate channel I2 is significant with a branching ratio of 100% to the environmental evolution of bromoxynil. The atmospheric lifetime (τ) of bromoxynil is given by 1/k_OH[OH], where k_OH is the overall rate constant. The atmospheric OH radical concentration [OH] is 9.7 × 10⁵ molecules cm⁻³.⁶² From the overall rate constant and the OH radical concentration, the lifetime of bromoxynil at 298 K is determined as 14 hours. This lifetime is in consistent with an earlier review report on bromoxynil which showed that the aerobic degradation of bromoxynil at 20 °C (i.e. 293 K) takes place in 16.5 hours.⁶³ In a recent study the lifetime of brominated diphenyl ether (BDE), which consists of an ether linkage with two bromine atoms was reported as 6.7 days.⁶⁴ As shown in Fig. S2,† the rate constant calculated for the intermediate, I1 show positive temperature dependence, whereas, the rate constant calculated for the intermediates, I2 and I3 show negative temperature dependence. This result reveals that the formation of intermediate, I1 occurs dominantly in the lower layers of the troposphere and the intermediates, I2 and I3 are formed in the upper layers of the troposphere.

4. Atmospheric implications

In summary, the present study focuses on the atmospheric degradation of bromoxynil by OH radical. Since polyhalogenated phenols are persistent organic pollutants and are probable human carcinogens,⁶⁵ the degradation of bromoxynil is of biological and environmental significance. In the present work, a prototype atmospheric degradation of bromoxynil and formation of secondary products is studied, which is useful in understanding the risk assessment of the atmospheric emission of bromoxynil. The reaction pathways corresponding to the formation of six intermediates of bromoxynil + OH radical reaction have been explored. These initially formed intermediates have sufficient energy to undergo subsequent reactions with other atmospheric oxidants. Of the six intermediates studied, the formation of 3,5-dibromo-2,4-dihydroxy benzonitrile (I1), 2,6-dibromo-4-cyanophenoxy radical (I2) and 2,6-dibromo-4-cyano-1-hydroxy benzene radical (I3) are found to be the most favorable with a small energy barrier. The initially formed radicals react with molecular oxygen resulting in the formation of peroxy, epoxy and bicyclic radicals. The peroxy radical reacts with HO₂, NO and NO₂ resulting in the formation of hydroperoxide adducts, alkoxy radical and nitroso compounds. The most favorable secondary reaction pathway from the intermediate, I1 is the formation of a seven-membered ring dihydroxy epoxide intermediate, I9. These highly soluble epoxides are responsible for the formation of organic aerosols. The intermediate, I9 further decomposes into HOBr, which is responsible for the formation of carcinogenic bromate ions in ozonized water. Tetrabromo-tetrahydrobenzo-cyclopenta-dioxepine-dicarbonitrile (TeBDD, P4) is formed with a small energy barrier of 11.52 kcal mol⁻¹ and it is the most favorable secondary reaction pathway from intermediate, I2. The most favorable secondary reaction pathway from intermediate, I3 is the formation of hydroperoxide adduct along with O₂ (P6). As discussed in previous sections, the initially formed radicals can undergo direct reaction with NO₂ yielding nitro brominated compounds. Also, these radicals can undergo oxidative coupling to form dibrominated compounds through a series of intermediates and transition states. The overall rate constant and the branching ratio calculated for the intermediates, I1, I2, and I3 show that the contribution of intermediate, I2 is significant in determining the environmental evolution of bromoxynil. The lifetime of bromoxynil is 14 hours, that is the reaction between bromoxynil and OH radical is the major atmospheric sink for bromoxynil. Note that the products formed from the secondary reactions are equally toxic as the parent bromoxynil, since their lifetime is expected to be more than that of parent bromoxynil. Hence, the use of bromoxynil as a herbicide should be limited.

Acknowledgements

L.S. is thankful to the Department of Science and Technology (DST), Govt. of India for awarding INSPIRE Fellowship. One of the authors (K.S.) is thankful to the University Grants Commission (UGC), Govt. of India for granting the research project under major research project. The authors thank the reviewers for giving valuable suggestions to improve the manuscript.

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Footnote

† Electronic supplementary information (ESI) available: The relative energy (ΔE in kcal mol⁻¹), enthalpy of reaction (ΔH in kcal mol⁻¹) and Gibb's free energy (ΔG in kcal mol⁻¹) of the reactive species involved in the studied reactions calculated using B3LYP and MPW1K methods are summarized in Tables S1–S4. The rate constant calculated using TST, TST/SCT and CVT methods are summarized in Table S5. The optimized structure of the transition states involved in the reaction of bromoxynil with OH radical and its subsequent reactions is illustrated in Fig. S1. The Arrhenius plot of the rate constant of the intermediates, I1, I2 and I3 over the temperature range of 278–350 K is shown in Fig. S2. See DOI: 10.1039/c3ra47334a

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